Which of the following numbers is a multiple of 8? ${56,66,94,105,106}$
Answer: The multiples of $8$ are $8$ $16$ $24$ $32$ ..... In general, any number that leaves no remainder when divided by $8$ is considered a multiple of $8$ We can start by dividing each of our answer choices by $8$ $56 \div 8 = 7$ $66 \div 8 = 8\text{ R }2$ $94 \div 8 = 11\text{ R }6$ $105 \div 8 = 13\text{ R }1$ $106 \div 8 = 13\text{ R }2$ The only answer choice that leaves no remainder after the division is $56$ $ 7$ $8$ $56$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $8$ are contained within the prime factors of $56$ $56 = 2\times2\times2\times7 8 = 2\times2\times2$ Therefore the only multiple of $8$ out of our choices is $56$. We can say that $56$ is divisible by $8$.